Head-on collision between two solitary waves in a compressible Mooney-Rivlin elastic rod

The interaction between two solitary waves in hyperelastic rods had been studied in literature by numerical methods, and here we study the head-on collision between two solitary waves in a circular cylindrical rod composed of a compressible Mooney-Rivlin material by a perturbation approach which combines the reductive perturbation method with the technique of strained coordinates. The third-order asymptotic solution which describes the evolution process of interaction is derived. It is found that the head-on collision does have imprints on the colliding waves with nonuniform phase shifts at O(ε²), which cause the tilting of the wave profiles. Our analytical results provide a formula for the maximum amplitude during the collision and also successfully explain the phenomenon that the smaller solitary wave has a larger distortion while the larger solitary wave has a smaller distortion. © 2000 Elsevier Science B.V.